Bipedal walking and running with spring-like biarticular muscles.

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated "dynamic walking" biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents "transversal" dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems. © The Author(s) 2011.

Minimalistic control of biped walking in rough terrain

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the "phase locking" mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain. © 2010 Springer Science+Business Media, LLC.

Stable dynamic walking over rough terrain: Theory and experiment

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated mechanical systems. An important example of such a system is an underactuated "dynamic walking" biped robot walking over rough terrain. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to higher degree-of-freedom robots over arbitrary terrain and other impulsive mechanical systems. © 2011 Springer-Verlag.

Bipedal walking and running with compliant legs

Passive dynamics plays an important role in legged locomotion of the biological systems. The use of passive dynamics provides a number of advantages in legged locomotion such as energy efficiency, self-stabilization against disturbances, and generating gait patterns and behavioral diversity. Inspired from the theoretical and experimental studies in biomechanics, this paper presents a novel bipedal locomotion model for walking and running behavior which uses compliant legs. This model consists of three-segment legs, two servomotors, and four passive joints that are constrained by eight tension springs. The self-organization of two gait patterns (walking and running) is demonstrated in simulation and in a real-world robot. The analysis of joint kinematics and ground reaction force explains how a minimalistic control architecture can exploit the particular leg design for generating different gait patterns. Moreover, it is shown how the proposed model can be extended for controlling locomotion velocity and gait patterns with the simplest control architecture. © 2007 IEEE.

Running and walking with compliant legs

It has long been the dream to build robots which could walk and run with ease. To date, the stance phase of walking robots has been characterized by the use of either straight, rigid legs, as is the case of passive walkers, or by the use of articulated, kinematically-driven legs. In contrast, the design of most hopping or running robots is based on compliant legs which exhibit quite natural behavior during locomotion. © 2006 Springer.